The love affair of wings and rubber!

Aerodynamics | Suspension

It may seem antithetic: Aerodynamics and tyre dynamics and yet a deeper understanding into the behaviour of wings and tyres may insinuate a strong connection. These two areas certainly have had some mystery in their past may it be the mysterious force of lift or grip offered by tyres. These two areas are certainly
fascinating which may seem ironic in the case of rubber, but when one dwells deeper it will certainly captivate one’s thought.

The linearity in the coefficient of lift v/s angle of attack curve of thin aerofoil sections is akin to the lateral force v/s slip angle curve in a tyre. This interesting connection may seem very subtle and perhaps inconclusive of their deep connection, but in the view of control systems this property is crucial and anything that a control systems engineer would love to work with. Well, as a matter of fact the linearity in the coefficient of lift v/s angle of attack curve has been proved in theory (thin aerofoil theory) as well as in practice however the same in the case of a tyre has no solid theoretical background but agrees well with experimental data.

Another alluring congruence between the two seems to take the same name perhaps for the similarity that it holds: Camber. Camber as in aerodynamics is the asymmetry of the aerofoil section above and below the dividing chord line. Camber with respect to tyre is its inclination in the rear view of a car. Although there can be no real similarities in their definitions, their effect is however to raise the above curves off the x-axis (either below or above depending on the sign of camber). A negative cambered aerofoil generally tends to change the momentum of the flow more aggressively than a
symmetrical aerofoil and hence the higher lift at the same angle of attack.
The penalty to this advantage is a lower stall angle in cambered aerofoils owing to earlier onset of separation catered by a more rigorous suction surface geometry. The reason for elevated lateral forces in a cambered tyre leaning into the curve can be accounted for by lateral distortion of the contact patch or the tire print. The camber thrust that is obtained is however more complex as it is a function of numerous variables like tyre type, tyre pressure, tread, load, tractive effort, camber and slip angle.

To add to the list is the induced drag which in wings is caused by the inclination of the lift vector by velocity induction by tip vortices and in tyres is because of the oblique incidence of the side force or the lateral force vector to the velocity vector.

The boundary layer over a wing can be thought of as analogous to the tire print where all the mystery remains concealed. The boundary layer is very thin, however it encloses within it very interesting concepts like the occirrence of Tollmein-Schilichting waves at the onset of turbulence during transition, the division of different layers within a turbulent boundary layer dictated by the values of viscous stresses and reynolds stresses , the law of wall critical in modelling of near wall flows, quassi periodic sequence of events resulting in hair-pin voritices and their susceptibility to Helmholtz’s instability within the viscous sub-layer and many such fascinating concepts. The tyre print on the other hand is in no way less sophisticated and involves hysterisis of compression and expansion of tyre tread to produce the asymmetrical lateral force distribution partly responsible for the mysterious aligning torque along with the mechanical trail. This hysterisis is also responsible for the asymmtric distribution of normal force in the tyre print. A less noticeable phenomenon is standing wave in a rolling tyre at high speeds caused by a delay in the tread emerging from the tire print snapping back to its orbit around the wheel and in case of excessive speed it may lead to a shock wave analogous to aerodynamics leading to disintegration of the tyre.

In all, these areas wear a façade trying to illustrate simplicity however are very abstruse when dealt with greater detail and hence race car companies, teams and its skilled engineers bestow a huge amount of money, time and its invaluable resources towards research aiming at just those fractions of a second that could prove vital in perhaps winning the championship.

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Indian Institute of Technology
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